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Conception Fabrication CommandeConception Fabrication Commande
Sajid Ullah BUTT
Conception et modélisation d'un montage de fabrication pour le balançage optimisé d'une famille de pièces
Arts et Métiers ParisTech - Centre de MetzLaboratoire de Conception Fabrication Commande EA 4495
Jury M. Cornel Mihai NICOLESCU, Professeur, KTH, Stockholm, Sweden RapporteurM. Jean-François RIGAL, Professeur, LAMCOS, INSA Lyon, France RapporteurM. Henri PARIS, Professeur, G.SCOP, Université Joseph Fourier, Grenoble, France ExaminateurM. Jean-François ANTOINE, Maitre de conférences, IUT de Nancy Brabois, France Co-directeur de thèseM. Patrick MARTIN, Professeur, LCFC, Arts et Métiers ParisTech, Metz, France Directeur de thèse
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Conception Fabrication CommandeConception Fabrication CommandePresentation layout
Sajid Ullah BUTT, PhD Defense 5 July 2012
• Context
• Positioning errors
• Compensation
• Objectives
• Workpiece repositioning through locators
• All the elements rigid
• Proposed fixturing system
• Analytical formulation
• Large displacements and Homogeneous Transformation Matrices
• Deformation of elastic elements and rigid body displacement of part on fixture under load
• Deformation of locators and contacts
• Lagrangian formulation
• Negligible friction, Small Displacements
• Convergence of non-linear contact deformation
• Work realized
• Conclusion
• Future work
Case Study
Context Kinematic Model
Mechanical Model
Conclusion and
Perspectives
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Conception Fabrication CommandeConception Fabrication CommandePresentation layout
Sajid Ullah BUTT, PhD Defense 5 July 2012
• Context
• Positioning errors
• Compensation
• Objectives
• Workpiece repositioning through locators
• All the elements rigid
• Proposed fixturing system
• Analytical formulation
• Large displacements and Homogeneous Transformation Matrices
• Deformation of elastic elements and rigid body displacement of part on fixture under load
• Deformation of locators and contacts
• Lagrangian formulation
• Negligible friction, Small Displacements
• Convergence of non-linear contact deformation
• Work realized
• Conclusion
• Future work
Case Study
Context Kinematic Model
Mechanical Model
Conclusion and
Perspectives
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
4/48
Conception Fabrication CommandeConception Fabrication Commande
R
Initial surface
R
Context
Optimal balancing• The final product should have a minimum
allowance for better machining• In case of perfect positioning, minimum rough part
radius should have to be r + h• ∆ is the positioning error between the final product
and the rough part’s central axis• The minimum radius of the rough part has to be R
for a good machining operation• More positioning error will increase the material
waste
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
∆
∆h
Allowance > Min chip thickness
h
Sajid Ullah BUTT, PhD Defense 5 July 2012
r
r
Final part
∆ L
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Conception Fabrication CommandeConception Fabrication Commande
Part
Pallet
Col
umn
Base
Spindle
Kinematics defects
Locators placement
Geometric/form defects
Deformation due to forces
Context
Workpiece/machine tool Positioning error • Variation among the parts of the same part family cause the positioning error during
fixturing• Positioning error of the workpiece affects the quality of the final product
Tool wearEffect of heatNC Code errors
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Tool
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
Possible placement of
locators
Placement of locators• Block the 6-DOFs of the partPlacement procedure
Choose the locating surfaces taking into account the constraints of accessibility, load, external force and movements (Somashekar 2002)
Select the locators configurations (3-2-1, 3-2-1C, etc.) Choose the locators positions for the part stability (Roy
& Liao, 2002; Zirmi et al. 2009)
Positioning errors
3-2-1
3-2-1C
4-1-1
(H. Paris, 1995)
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Y
-Y
Z
-X X
-Z
0
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
Geometrical and form defects• When workpiece is placed directly on the locators• Local geometrical defects cause the orientation error • The orientation error have more effect on the final product quality than the
translation error (Asante, 2009)
Positioning errorsCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
F
Deformation of locators under external load• The locators and their contacts deform under clamping and machining
forces• Deformation depends upon the stiffness of the locators• Hertz contact theory may be applied to calculate the contact deformation• Locators deformations induce the workpiece displacement
Zero contact deformation
sph
C
Including contact deformation
Positioning errorsCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Z
Y
X
F FF
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandePositioning errors
Machine tool/kinematic chain defects• Machine tool position uncertainty • Kinematic chain • Kinematic defects increase with the increase the
number of machine axes
Other Defects• Defects due to heat generation• NC code defects• Tool wear
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
How to Compensate these errors?
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Conception Fabrication CommandeConception Fabrication CommandeError compensation
Existing methods• Changing the part program
• Easiest way (Ramesh et al. 2000)• Orientation of the machine tool Disadvantages• Need 4 or 5 axis machines• Very expensive for the existing production
line
Actual position
Ideal position
Compensated position
(Zhu et al. 2012)
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Base
PartPart
Tool
Col
umn
Pallet
Part programTool orientation
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Conception Fabrication CommandeConception Fabrication Commande
Base
Tool
Col
umn
Part
Part
Baseplate
Part
Baseplate
Pallet
6 DOF repositioning
Error compensationCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Our proposal• A 6-DOF workpiece repositioning
system is proposed
• A baseplate is introduced to avoid the positioning error caused by the geometrical defects
• Repositioning is performed through the positioning of the 6 locators
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Conception Fabrication CommandeConception Fabrication Commande
• Develop a fixturing system which can– Hold custom single and complex parts– Perform 6-DOF Repositioning of the part at desired position – Added to Single machine unit or production/assembly line – Minimum modifications on existing production line
Part
Baseplate
Tool
Part
Baseplate
Conveyor
Previous Workstation
Reconfigurable Pallet
Base
Col
umn
Pallet
ObjectiveCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Single machine unit Production/Assembly line
Sajid Ullah BUTT, PhD Defense 5 July 2012
Measure Calculate Compensate
Part
Baseplate
Reconfigurable Pallet
Part
Baseplate
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Conception Fabrication CommandeConception Fabrication Commande
MeasureWorkpiece geometrical errors• Offline: using CMM• Online: Integrated sensors
Calculate• The advancement of locators required to compensate the errors using Homogeneous
Transformation Matrices and Large displacements (Kinematic model)• The errors due to deformation of elastic elements under load using Small Displacement
hypothesis (Mechanical model)
CompensateThrough the axial advancement of 6 locators• Geometrical errors • Mechanical errors
ObjectiveCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Error compensation principle
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Conception Fabrication CommandeConception Fabrication CommandePresentation layout
Sajid Ullah BUTT, PhD Defense 5 July 2012
• Context
• Positioning errors
• Compensation
• Objectives
• Workpiece repositioning through locators
• All the elements rigid
• Proposed fixturing system
• Analytical formulation
• Large displacements and Homogeneous Transformation Matrices
• Deformation of elastic elements and rigid body displacement of part on fixture under load
• Deformation of locators and contacts
• Lagrangian formulation
• Negligible friction, Small Displacements
• Convergence of non-linear contact deformation
• Work realized
• Conclusion
• Future work
Case Study
Context Kinematic Model
Mechanical Model
Conclusion and
Perspectives
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
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Conception Fabrication CommandeConception Fabrication Commande
Objective• Repositioning of a part of a part family placed roughly with a precision of
some millimeters Components
– Part (Hip prosthesis)– Baseplate (Cuboid)– 6-Locators (Axial movement)– Pallet
All the elements are rigid
XZ
Y O(Machine/Pallet reference)
P
6 4
5
2
31
Baseplate
part
Kinematic modelCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Part
Baseplate
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Conception Fabrication CommandeConception Fabrication Commande
[PPF
] = [P
bb’]
XF
Xb’
XO
Xb
XP
[PPF]
[PbP]
[Pb’F]=[PbP]
[POb’] [POb]
Correction[PPF ]
Error to be corrected
Rigid link
Baseplate correction
through locators
Initial baseplate placement on the locators
Formulation
XZ
Y O(Machine/Pallet reference)
Y3
Z3
X3
b
P
XP
ZPYP
6 4
5
2
31
Baseplate
part
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Baseplate Surface normals
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Conception Fabrication CommandeConception Fabrication Commande
CPT 12/14 Hip Prosthesis Zimmer
-10.00 10.00 30.00 50.00 70.00 90.00 110.00 130.000.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
Initial Position of the workpiece (2D Simulation)
Min Material (Chebyshev)
RMS
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
P
Sajid Ullah BUTT, PhD Defense 5 July 2012
Y
X
• Point P (intersection of two centerlines)• Definition of a plane• Simulation in 2D
Stem
Neck
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Conception Fabrication CommandeConception Fabrication Commande
-10.00 10.00 30.00 50.00 70.00 90.00 110.00 130.000.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
PMin Material (Chebyshev)
RMS
• Point P (intersection of two centerlines)• Definition of a plane• Simulation in 2D
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Y
X
Initial Position of the workpiece (2D Simulation)
Stem
Neck
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Conception Fabrication CommandeConception Fabrication Commande
Z
X
1*2*
1’2’
1 2
Final calculated Position
Calculating point of contact in axis
Position calculation in 3D
Compensation of errorsCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
2D Schematic explanation
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Conception Fabrication CommandeConception Fabrication CommandeSimulation procedure: CAD ModelingCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Inverse impression of the workpiece for the simulation of
cutting tool path D=3mm
Cavity with original workpiece dimensions
Baseplate
Pallet
Workpiece
Sajid Ullah BUTT, PhD Defense 5 July 2012
Boolean Operation
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Conception Fabrication CommandeConception Fabrication CommandeCase study
Initial Data
Final required part position
Calculated positions of locators
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Gray: Machined surfaceOrange: Rough surface
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
Simulated machining
Positioning error of workpiece after correction
Case study
Calculated positions of locators
Final Product
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Calculated positions of locatorsPositioning error of workpiece after second side correction
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Conception Fabrication CommandeConception Fabrication CommandeRobustness of model/Sensitivity Analysis
• Use of Plucker matrix• Precision of workpiece displacement as a function of locators’ positioning precision• Position uncertainty = Geometrical uncertainty + uncertainty due to temperature
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sensitivity analysis
Sajid Ullah BUTT, PhD Defense 5 July 2012
Worst case
Precision of locator
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Conception Fabrication CommandeConception Fabrication CommandePresentation layout
Sajid Ullah BUTT, PhD Defense 5 July 2012
• Context
• Positioning errors
• Compensation
• Objectives
• Workpiece repositioning through locators
• All the elements rigid
• Proposed fixturing system
• Analytical formulation
• Large displacements and Homogeneous Transformation Matrices
• Deformation of elastic elements and rigid body displacement of part on fixture under load
• Deformation of locators and contacts
• Lagrangian formulation
• Negligible friction, Small Displacements
• Convergence of non-linear contact deformation
• Work realized
• Conclusion
• Future work
Case Study
Context Kinematic Model
Mechanical Model
Conclusion and
Perspectives
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
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Conception Fabrication CommandeConception Fabrication CommandeMechanical model
• Clamping and machining forces and moments• Elements designed to be rigid
– Workpiece baseplate assembly– Mass elements
• Elastic elements– Locators (body and contact)– Baseplate at contacts– Clamps with imposed external displacements
• Small displacement hypothesis• Friction neglected• Effects of heat neglected• No slippage of clamps at contact
{XE}2
Z
XY
P
[K]1
[K]2
[K]3[K]4
[K]5[K]6
{XE}1
[KE]2
[KE]1f
| T, F |
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandeFormulation
XF*
Xb*
XF
Xb’
XO
P b’F =
P bP
Pob*
P b*F*
=P bP
POb’
Pb*b’
PFF*
Rigid link
Correction through locators
Error of the workpiece under load Machining forces and their displacement
P b’b*
=PFF
*
Clamping forces and their
displacements
Initial baseplate locating under load
Correction
{XE}2
Z
XY
P
[K]1
[K]2
[K]3[K]4
[K]5[K]6
{XE}1
[KE]2
[KE]1f
| T, F |
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandeFormulation
Work done by external force
Lagrangian Equation
Z
X
Y21
3
K3
6
K6
P
ZP
XP
YP
5
K5
4
K4
K2K1
Baseplate KE1
XE1
KE2
XE2
Part
F
T
Machine/Pallet Reference
{ΔX,ΔY,ΔY}T: Linear displacement vector of point P{Δα,Δβ,Δγ}T: Angular displacement vector of point P{F}: Force vector{T}: Moment vector
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
U: Potential energy of the systemT: Kinetic energy of the systemW:Work done by the external forcesqi: Generalized coordinates
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandeFormulation
Potential Energy: U
Lagrangian Equation
Kinetic Energy: T tZV
tYV
tXV
z
y
x
tt
tt
tt
z
y
x
Z
X
Y21
3
K3
6
K6
P
ZP
XP
YP
5
K5
4
K4
K2K1
Baseplate KE1
XE1
KE2
XE2
Part
F
T
Machine/Pallet Reference
Locators
Clamps
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
(Lalanne et al. 1986)
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
Locator Pin
68mm
20mm
20mm
Locator model
• Screw-nut Wedge-slop locator • Rotation of knob causes axial
movement of locatorSlope 1:2Screw M6x1 Locator diameter: 20mmLength of locator: 68mmSphere radius: 20mm
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Perforated plate Pitch = 40mm
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
1
2aL tLk k
Initial position of the surface
Final position of the surface
Locator axis
sph
ni
ZY
X
Deformed locator at the position having minimum potential energy
Formulation (Zero Friction)CONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
3
aL tLk k
4tL
aL
Bending + Shear
Compression
Minimum energy (Menabrea’s theorem) Potential energy of locators
Locator’s Stiffness Matrix
Sajid Ullah BUTT, PhD Defense 5 July 2012
sph
tL
aL
0U
tL
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Conception Fabrication CommandeConception Fabrication Commande
Final position of contact surface after only locator deformation
C
ni
Final position of contact surface after locator and contact deformation
ni
ZY
X Zero contact deformation
Including contact deformation
Formulation
Deformation of contact (Hertz contact theory)CONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandeFormulation (Iterations procedure)
New stiffness matrices of each locator [K]i
Stiffness matrix [K] , overall displacement vector {∆X} and natural frequencies of the system using Lagrangian
Deformation of each locator{δ}i
Potential energy calculations
Deformation and stiffness of ith
locator body (δL, KL) i
Deformation and stiffness of ith contact (δC, KC) i
Overall stiffness of each locator and displacement vector of the workpiece ({∆Xnew} ) using inverse Plucker
[KNew]i = {F}i /{δNew}iT
{∆XNew}=[Plu]-1{δPlu}
Limite1001
XX
MAX New
iii KF
Final deformation/displacement vector and stiffness matrix of each locator and the
fixturing system
No
Yes/STOP
Kinetic energy and Work done
[K]i =[KNew]i
{∆X}= {∆XNew} +gain*({∆X} - {∆Xnew} )
{δNew}i= {δC}i +{δL}i
{∆XNew}
{∆XNew}
[K]i
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
ni
ZY
X
3D stiffness matrix of the locator body
[KL] i
[KC] i
{F}i
3D stiffness matrix of the contact
3D equivalent stiffness matrix
{F}i
[KNew] i
Force vector on the ith locator
{F}i
Sajid Ullah BUTT, PhD Defense 5 July 2012
Gain
33/48
Conception Fabrication CommandeConception Fabrication Commande
Y
X
Z
1
2
3
4
5 6
P
70
110
70
110
14
1008
60
23
21
60
60 60
100
22
10
12040
O
{XE}2
Z
XY
P
[K]1
[K]2
[K]3[K]4
[K]5[K]6
{XE}1
[KE]2
[KE]1f
Case study
oB
oB
oB
494.0
485.1
039.1
| T, F |
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
34/48
Conception Fabrication CommandeConception Fabrication Commande
Clamps
Baseplate (made of steel)
{XE}2
Z
XY
P
[K]1
[K]2
[K]3[K]4
[K]5[K]6
{XE}1
[KE]2
[KE]1f
locators-baseplate contacting points
Contacting points of clamps
Case study (Input)
Locator stiffness| T, F |
68mm
20mm
20mm
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Ext
ract
ed fr
om
CA
D m
odel
35/48
Conception Fabrication CommandeConception Fabrication Commande
Processed material• Prosthesis material : M30NW (X4CrNiMoN21)• ISO equivalent material: M3.2.C.AQ (Stainless steel Cast, Annealed quenched)
– Stainless steel 316LN (X2CrNiMoN18-13, Sandvik technical guide 2011)– σ = 880MPa
Cutting condition– Tool : CoroMill 216 ball nose endmill of 3 mm in diameter (2 teeth)– DOC, ap : 0.5 mm, Feed per tooth, Fz : 0.03 mm– Cutting speed, Vc: 75 m/min, Spindle speed, N : 8000 RPM
Machining forces– Tangential force (Sandvik technical guide 2011)– Repulsive forces (Pruvot, 1993)
Case study (Input)CONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication Commande
Results without considering contact deformation
Case study (Results)
Results with considering contact deformation
Natural frequencies of the system Error compensation
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
Tool Excitation frequency=837 rad/sec
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Conception Fabrication CommandeConception Fabrication Commande
1 10 100 10001E-02
1E-01
1E+00
1E+01
1E+02
1E+03
∆X∆Y∆Z∆β∆γ∆α
1 10 100 1000-70
-20
30
80
130
∆X∆Y∆Z∆β∆γ∆α
Convergence of displacement vectorμR
ad, μ
m
No of iterations
No of iterations
% E
rror
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
38/48
Conception Fabrication CommandeConception Fabrication Commande
1 10 100-60
-40
-20
0
20
40
60
80
100
120
140
0.330.410.510.640.801.00
GAIN
Effect of gain on convergence μR
ad
No of iterations
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Convergence of parameter slowest parameter ∆γ
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandeRough contactsCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
Baseplate-locator equivalent RMS roughness = 0.8 E-6 m
k C/k
H
RMS Roughness (m)
1N
10N
100N
1kN
Comparison between ideal and rough surface contacts
(Bahrami et al. 2005)
Sajid Ullah BUTT, PhD Defense 5 July 2012
6.6% decrease
40/48
Conception Fabrication CommandeConception Fabrication Commande4-2-2 locator configuration
{XE}2
Z
X
Y
P
[K]1
[K]2
[K]3[K]4
[K]5
[K]6
{XE}1
[KE]2
[KE]1
f
| T, F |
{XE}2
Z
X
Y
P
[K]1
[K]2
[K]3
[K]4
[K]5
[K]6
{XE}1
[KE]2
[KE]1
f[K]7
[K]8
| T, F |System stiffness
Comparison between 3-2-1 and 4-2-2
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandePresentation layout
Sajid Ullah BUTT, PhD Defense 5 July 2012
• Context
• Positioning errors
• Compensation
• Objectives
• Workpiece repositioning through locators
• All the elements rigid
• Proposed fixturing system
• Analytical formulation
• Large displacements and Homogeneous Transformation Matrices
• Deformation of elastic elements and rigid body displacement of part on fixture under load
• Deformation of locators and contacts
• Lagrangian formulation
• Negligible friction, Small Displacements
• Convergence of non-linear contact deformation
• Work realized
• Conclusion
• Future work
Case Study
Context Kinematic Model
Mechanical Model
Conclusion and
Perspectives
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
42/48
Conception Fabrication CommandeConception Fabrication CommandeConclusion
• High quality baseplate is introduced• Compensation is performed through advancement of locators (kinematic model)• Deformation of each locator is calculated and its contact with baseplate under load (mechanical model)• Also its resultant rigid body displacement of the workpiece is calculated (positioning error)• Compensation is performed using kinematic model
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Base
Tool
Col
umn
Part
Part
Baseplate
Part
Baseplate
Pallet
Kinematics defects
Locators placement
Geometric/form defectsDeformation due to forces
Sajid Ullah BUTT, PhD Defense 5 July 2012
6 DOF part repositioning
43/48
Conception Fabrication CommandeConception Fabrication CommandeConclusion
6 DOF positioning using kinematic model– 3-2-1 locating configuration is used– All elements are considered rigid– Error compensation is performed through the axial translation of 6-locators
using HTM and LD– Validated on a case study of repositioning the hip prosthesis– Sensitivity analysis are carried out
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
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Conception Fabrication CommandeConception Fabrication CommandeConclusion
Mechanical modeling of the fixturing system– The analytical model is developed– Deformation of locators under load is calculated – Workpiece-baseplate assembly is designed to be rigid– Locators, clamps and locator-baseplate contacts are assumed deformable– Small displacement hypothesis are used– Lagrangian formulation is used to calculate the mass & stiffness matrices and workpiece
displacement vector– Non-linear behavior of locator-baseplate contact is linearized– Demonstrated on a case study of 3-2-1 locating configuration and compared with 4-2-2
configuration of locators
CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION
Sajid Ullah BUTT, PhD Defense 5 July 2012
45/48
Conception Fabrication CommandeConception Fabrication Commande
• Analytical modeling gives very quick result as compared to numerical modeling
• The proposed mechanical model can easily be applied to more complex problems with multiple loads, different orientations and stiffness of locators and clamps
• The proposed fixturing system allows precise positioning of the workpiece at each workstation without the need of 4 or 5 axis machines or modifying the existing workstations
• Reduce dimensional errors, machining allowances and thus the material removal by uniformly centering the rough part to the required part• Consequently, it reduces the material waste
• Large parts could also be repositioned during assembling
ConclusionCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
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• The positioning error due to heat/temperature change can be introduced
• Construction of the fixturing system for validating the analytical model. We could not construct the model because of time and cost associated with precise part production
• The mechanical model calculates the deformation of locators as the result of an instantaneous force at a point. The model should be developed to simulate the whole tool path
Limitations and Future workCONTEXT KINEMATIC MODEL MECHANICAL
MODEL CONCLUSION
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Conception Fabrication CommandeConception Fabrication CommandeScientific activities
Poster Presentation
• “Conception, Modélisation et Réalisation d'un montage modulaire rapide destine a la Fabrication Mécanique” J2A Arts et Métiers ParisTech, 8th-9th June 2010 (Poster Presentation)
National Colloquium
• S. U. Butt, J. F. Antoine, P. Martin, “Mechanical model for control of 6 DOF repositioning system”, 12th National Colloquium, AIP Primeca, Mont-Dore 29th March to 1st April 2011
Scientific Publications
• S. U. Butt, J. F. Antoine, P. Martin, “An analytical model for the repositioning of 6 DOF repositioning system”, Journal of Mechanics and Industry (Accepted June 2012 )
• S. U. Butt, J. F. Antoine, P. Martin, “An analytical stiffness model for spherical rough contacts”, Asian International Journal of Science and Technology in Production and Manufacturing Engineering (Submitted June 2012)
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